Answer:
Part 1) 
Part 2) 
Part 3) 
Part 4) 
Part 5) 
Part 6) 
Part 7) 
Part 8) 
Step-by-step explanation:
we know that
The formula to calculate the sum of the interior angles of a convex polygon is equal to

where
n is the number of sides of the polygon
Part 1) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 540°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 2) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,080°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 3) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,800°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 4) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 1,620°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 5) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 2,340°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 6) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 3,600°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 7) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 2,880°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides

Part 8) Find the number of sides of a convex polygon if the sum of the measures of its interior angles is: 7,560°
we have

substitute in the formula

solve for n
Divide by 180° both sides

Adds 2 both sides
